Emery comes from the Germanic Amalric — composed of amal (work, labour) and ric (ruler, power), meaning "industrious ruler" or "work-ruler." The name was traditionally male and arrived in England with the Normans.
Emery as a girl's name is a recent American phenomenon, entering the U.S. top 1000 in 2010. It now sits in the U.S.
Emery does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
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In Pythagorean numerology the letters of Emery reduce to 3, The Communicator. This is a traditional interpretive system, not a factual claim about the name.